Emily Analysis

**Table 1. Baseline Characteristics**
Characteristic	Overall N = 180¹	ABC N = 30¹	ACB N = 30¹	BAC N = 30¹	BCA N = 30¹	CAB N = 30¹	CBA N = 30¹	p-value²
Age (years)	32 (8) [18, 45]	33 (8) [19, 44]	31 (7) [18, 42]	31 (7) [20, 44]	33 (8) [19, 45]	32 (7) [21, 44]	31 (7) [20, 44]	0.6
Race								0.9
Black	64 (36%)	12 (40%)	13 (43%)	12 (40%)	10 (33%)	8 (27%)	9 (30%)
White	52 (29%)	8 (27%)	9 (30%)	7 (23%)	7 (23%)	12 (40%)	9 (30%)
Other	64 (36%)	10 (33%)	8 (27%)	11 (37%)	13 (43%)	10 (33%)	12 (40%)
Female	81 (45%)	13 (43%)	11 (37%)	16 (53%)	14 (47%)	12 (40%)	15 (50%)	0.8
¹ Mean (SD) [Min, Max]; n (%)
² Kruskal-Wallis rank sum test; Pearson’s Chi-squared test

preliminary assessment and comparison of systemic and local Pharmacokinetics (PK) of Pill A, Gel B, and Gel C

No apparent difference in starting value by period or treatment, so looking at change from baseline in PK

Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit

Blood PK Change by Treatment

Notation: \(i =\) subject, \(j =\) treatment,

\[ \begin{align} Y_{ij} &= \mu + \tau_1\text{I(Gel B)} + \tau_2\text{I(Gel C)} + b_{i} + \varepsilon_{ij},\\ b_{ij} &\sim N(0, \sigma_i^2), \\ \varepsilon_{ij} &\sim N(0, \sigma^2), \end{align} \]

Findings: Significantly less decrease in gels vs pill A

##             Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model           1  5 9718.129 9743.052 -4854.064                        
## model_large     2  8 9721.615 9761.493 -4852.807 1 vs 2 2.513838  0.4728

## Linear mixed-effects model fit by maximum likelihood
##   Data: baseline_long 
##        AIC      BIC    logLik
##   9718.129 9743.052 -4854.064
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:    11.76905 19.69016
## 
## Fixed effects:  bloodVL_change ~ treatment 
##                    Value Std.Error  DF  t-value p-value
## (Intercept)    121.16111  1.360734 898 89.04097       0
## treatmentGel B -10.88889  1.469661 898 -7.40912       0
## treatmentGel C -11.65556  1.469661 898 -7.93078       0
##  Correlation: 
##                (Intr) trtmGB
## treatmentGel B -0.54        
## treatmentGel C -0.54   0.50 
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.40327599 -0.57002844  0.04432071  0.61132413  2.48072577 
## 
## Number of Observations: 1080
## Number of Groups: 180

Skin PK Change by Treatment

Findings: Significantly less decrease in gels vs pill A

##             Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model           1  5 10773.34 10798.26 -5381.670                        
## model_large     2  8 10778.04 10817.92 -5381.022 1 vs 2 1.295485  0.7302

## Linear mixed-effects model fit by maximum likelihood
##   Data: baseline_long 
##        AIC      BIC   logLik
##   10773.34 10798.26 -5381.67
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:    15.67261 32.86382
## 
## Fixed effects:  skinVL_change ~ treatment 
##                    Value Std.Error  DF   t-value p-value
## (Intercept)    205.52778  2.092094 898  98.24021       0
## treatmentGel B -32.40556  2.452934 898 -13.21094       0
## treatmentGel C -41.92222  2.452934 898 -17.09065       0
##  Correlation: 
##                (Intr) trtmGB
## treatmentGel B -0.586       
## treatmentGel C -0.586  0.500
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -2.99812316 -0.62341504  0.04451491  0.66568981  2.81739908 
## 
## Number of Observations: 1080
## Number of Groups: 180

assess the correlation of PK with adherence measures and the occurrence of adverse events

Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit

Q: include treatment X adherence and treatment X AE interaction terms???

Skin PK

Skin/Blood PK ~ Random Intercept (Subject) + Treatment + Adherence + Carryover + Period

##              Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model            1  7 5307.160 5337.201 -2646.580                        
## model_large2     2 11 5290.549 5337.757 -2634.275 1 vs 2 24.61057  0.0001

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##       AIC      BIC   logLik
##   5307.16 5337.201 -2646.58
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev: 0.003649564 32.52911
## 
## Fixed effects:  skinVL_change ~ treatment + overall_adhere + overall_safety 
##                     Value Std.Error  DF    t-value p-value
## (Intercept)     162.22787  7.582825 356  21.394119       0
## treatmentGel B  -24.41464  3.625130 356  -6.734832       0
## treatmentGel C  -36.99593  3.543320 356 -10.441036       0
## overall_adhere    1.81506  0.274724 356   6.606870       0
## overall_safety1 -55.77639  5.201704 356 -10.722715       0
##  Correlation: 
##                 (Intr) trtmGB trtmGC ovrll_
## treatmentGel B  -0.509                     
## treatmentGel C  -0.443  0.534              
## overall_adhere  -0.945  0.311  0.234       
## overall_safety1  0.139 -0.079 -0.032 -0.205
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.43058828 -0.67881147  0.02915247  0.64404884  3.53027310 
## 
## Number of Observations: 540
## Number of Groups: 180

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##        AIC      BIC    logLik
##   5290.549 5337.757 -2634.275
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev: 0.004174974 31.79624
## 
## Fixed effects:  skinVL_change ~ treatment * overall_adhere + treatment * overall_safety 
##                                     Value Std.Error  DF   t-value p-value
## (Intercept)                     238.04771 21.667665 352 10.986311  0.0000
## treatmentGel B                 -108.95724 23.377772 352 -4.660719  0.0000
## treatmentGel C                 -122.25653 23.950925 352 -5.104460  0.0000
## overall_adhere                   -1.13762  0.818852 352 -1.389291  0.1656
## overall_safety1                 -29.61261  8.743642 352 -3.386759  0.0008
## treatmentGel B:overall_adhere     3.40490  0.904914 352  3.762682  0.0002
## treatmentGel C:overall_adhere     3.39045  0.924719 352  3.666464  0.0003
## treatmentGel B:overall_safety1  -40.84761 12.155471 352 -3.360430  0.0009
## treatmentGel C:overall_safety1  -37.04463 12.856933 352 -2.881296  0.0042
##  Correlation: 
##                                (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B                 -0.927                                          
## treatmentGel C                 -0.905  0.838                                   
## overall_adhere                 -0.993  0.921  0.899                            
## overall_safety1                 0.114 -0.106 -0.103 -0.148                     
## treatmentGel B:overall_adhere   0.899 -0.986 -0.813 -0.905  0.134              
## treatmentGel C:overall_adhere   0.880 -0.815 -0.988 -0.886  0.131  0.801       
## treatmentGel B:overall_safety1 -0.082  0.117  0.074  0.107 -0.719 -0.171 -0.094
## treatmentGel C:overall_safety1 -0.078  0.072  0.111  0.101 -0.680 -0.091 -0.158
##                                tGB:_1
## treatmentGel B                       
## treatmentGel C                       
## overall_adhere                       
## overall_safety1                      
## treatmentGel B:overall_adhere        
## treatmentGel C:overall_adhere        
## treatmentGel B:overall_safety1       
## treatmentGel C:overall_safety1  0.489
## 
## Standardized Within-Group Residuals:
##          Min           Q1          Med           Q3          Max 
## -3.405995796 -0.615618058  0.002664942  0.610769689  3.605667548 
## 
## Number of Observations: 540
## Number of Groups: 180

Blood PK

##              Model df      AIC      BIC    logLik   Test  L.Ratio p-value
## model            1  7 4860.258 4890.299 -2423.129                        
## model_large2     2 11 4851.039 4898.246 -2414.519 1 vs 2 17.21954  0.0018

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##        AIC      BIC    logLik
##   4860.258 4890.299 -2423.129
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:     4.74164 21.00209
## 
## Fixed effects:  bloodVL_change ~ treatment + overall_adhere + overall_safety 
##                     Value Std.Error  DF   t-value p-value
## (Intercept)      98.73209  5.172962 356 19.086184  0.0000
## treatmentGel B   -6.81051  2.354117 356 -2.893020  0.0041
## treatmentGel C   -9.10003  2.295483 356 -3.964320  0.0001
## overall_adhere    0.93216  0.187884 356  4.961396  0.0000
## overall_safety1 -26.34806  3.460017 356 -7.615009  0.0000
##  Correlation: 
##                 (Intr) trtmGB trtmGC ovrll_
## treatmentGel B  -0.513                     
## treatmentGel C  -0.443  0.538              
## overall_adhere  -0.949  0.327  0.247       
## overall_safety1  0.131 -0.079 -0.032 -0.195
## 
## Standardized Within-Group Residuals:
##           Min            Q1           Med            Q3           Max 
## -3.5553528690 -0.5673073777  0.0005900677  0.6043037231  3.0550971969 
## 
## Number of Observations: 540
## Number of Groups: 180

## Linear mixed-effects model fit by maximum likelihood
##   Data: merged 
##        AIC      BIC    logLik
##   4851.039 4898.246 -2414.519
## 
## Random effects:
##  Formula: ~1 | ptid
##         (Intercept) Residual
## StdDev:    5.176441 20.56066
## 
## Fixed effects:  bloodVL_change ~ treatment * overall_adhere + treatment * overall_safety 
##                                    Value Std.Error  DF   t-value p-value
## (Intercept)                    131.74236 14.431943 352  9.128525  0.0000
## treatmentGel B                 -39.19101 15.315595 352 -2.558895  0.0109
## treatmentGel C                 -52.11513 15.650359 352 -3.329964  0.0010
## overall_adhere                  -0.36462  0.545375 352 -0.668563  0.5042
## overall_safety1                -11.39117  5.811353 352 -1.960158  0.0508
## treatmentGel B:overall_adhere    1.31391  0.591905 352  2.219795  0.0271
## treatmentGel C:overall_adhere    1.73440  0.603583 352  2.873511  0.0043
## treatmentGel B:overall_safety1 -25.67859  8.049524 352 -3.190076  0.0016
## treatmentGel C:overall_safety1 -17.98165  8.518057 352 -2.111003  0.0355
##  Correlation: 
##                                (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B                 -0.924                                          
## treatmentGel C                 -0.901  0.841                                   
## overall_adhere                 -0.993  0.919  0.895                            
## overall_safety1                 0.113 -0.109 -0.107 -0.147                     
## treatmentGel B:overall_adhere   0.895 -0.986 -0.816 -0.901  0.138              
## treatmentGel C:overall_adhere   0.875 -0.818 -0.988 -0.881  0.135  0.804       
## treatmentGel B:overall_safety1 -0.080  0.118  0.075  0.104 -0.717 -0.173 -0.096
## treatmentGel C:overall_safety1 -0.075  0.073  0.113  0.098 -0.678 -0.093 -0.160
##                                tGB:_1
## treatmentGel B                       
## treatmentGel C                       
## overall_adhere                       
## overall_safety1                      
## treatmentGel B:overall_adhere        
## treatmentGel C:overall_adhere        
## treatmentGel B:overall_safety1       
## treatmentGel C:overall_safety1  0.492
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -3.63070078 -0.59111860 -0.02603496  0.59219448  2.76927257 
## 
## Number of Observations: 540
## Number of Groups: 180